Thank you very much for your insightful and important question. As we previously discussed in our Response to Weakness 2, the only difference between the Absolute and Confidence-Verb methods is the addition of a confidence prefix (i.e., uncertainty score prefix) to known questions. We would like to provide a detailed analysis to explain the advantages of Confidence-Verb over Absolute.
(1) Regarding honesty-related scores:
In our Response to Weakness 2, we emphasized that **the confidence prefix "enables the model to implicitly learn to more precisely capture its knowledge boundaries".** To substantiate this claim, we first calculate the *expected accuracy* of the unaligned model on the TriviaQA evaluation dataset, and then examine the distribution of *idk samples* after aligning the model using both Absolute and Confidence-Verb:
- *Expected accuracy* is defined as to the ratio of correct responses among m sampled responses (m=10 and temperature=1.0), as specified in Lines 183-184.
- *Idk samples* refer to evaluation samples where the aligned model replies with an idk response.
The results are presented in the table below. The first row represents the unaligned model's expected accuracy. The second and third rows display the distribution of idk samples across different expected accuracies for Absolute and Confidence-Verb, respectively.
| Methods \ Expected Accuracy | 0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1.0 |
|-----------------------------|---|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| Absolute | 35.54% | 9.91% | 6.55% | 5.18% | 4.38% | 4.38% | 3.59% | 4.27% | 5.98% | 7.18% | 13.04% |
| Confidence-Verb | 39.75% | 9.45% | 6.59% | 5.57% | 3.78% | 4.22% | 3.30% | 4.51% | 4.80% | 5.87% | 12.17% |
From the results, we can see that 39.75% of idk samples for Confidence-Verb occur when the unaligned model fails to provide a correct answer in all 10 attempts, compared to 35.54% for Absolute. More strikingly, the proportions of idk samples for expected accuracy < 0.4 and expected accuracy >= 0.4 are 57.18%:42.82% and 61.36%:38.65%, respectively, for Absolute and Confidence-Verb. This indicates that Confidence-Verb indeed more accurately identifies questions with lower confidence and refuses to answer them, thereby significantly improving the prudence score and ultimately, the overall honesty score.
(2) Regarding accuracy:
You have raised an excellent point, and we acknowledge that the effects of the computational load during inference cannot be completely ignored; in fact, accuracy is likely the result of multiple factors intertwined. We would like to highlight another significant factor contributing to the relatively low accuracy of Absolute: "fine-tuning LLMs on weakly known knowledge encourages hallucinations", as evidenced by [1]. Specifically, Section 5 and Table 2 of [1] illustrate that:
> ... Unknown fine-tuning examples **increase the risk of overfitting.** We now observe that this also applies to WeaklyUnknown, though to a lesser degree... This highlights that the decrease in performance is strongly attributed to **an increased rate of hallucinations.**
In our experiments, particularly with training samples with an expected accuracy of 0.1 (i.e., the WeaklyUnknown samples in [1]), Absolute *directly* instructs the model to learn correct responses, which **paradoxically encourages hallucinations instead of grounding in its pre-existing knowledge. Confidence-Verb mitigates this issue by incorporating an explicit confidence prefix.**
Fully unraveling the factors for improvement may require more extensive efforts and is worth discussing in future work. We can supplement this analysis in the revised version of our paper, and we sincerely welcome for further discussion.
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[1] Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations? https://arxiv.org/abs/2405.05904